= t1 [0, -1/3, 0, 1]
(page cut off)
Removed from the final exam.
Corrections are change R^4 to
to R^5 and text
"of the matrix" to
"of some matrix"
x
x
x
Solution: Find the RREF of A. It has 2 pivots. No test applies to
prove the columns are independent, because the columns of A are
dependent.
Also possible: Apply the Kernel Theorem, which says that a system
of linear homogeneous algebraic equations has solution set which
is a subspace.
Checked with maple. The answer
given here is correct.
An eigenspace may have multiple vectors found as Strang's Special solutions
which are not orthogonal. Gram-Schmidt is applied to these vectors to replace
the eigenspace basis by an orthogonal basis.